We issue them with our property management company as payer. I don't think we PMs have authority to issue 1099 on behalf of someone else.
Actually, consider this: We have a few clients (very small minority) that operate as following. We get paid fees in a fixed amount per month for their properties. We also collect rent checks made payable directly to the owners, and deposit the checks in their account. They also write sizable checks to us, which we keep in escrow. As vendors need to be paid, we pay them out of that escrow.
So the net result is, we never write these owners a check. Ever. The rents collected never touch our books, and we never issue them a 1099. We don't even have a W9 for them. How would I ever issue a 1099 to vendors in their name? We don't even have their social sec (actually in this case the EIN # of their LLC). Okay, unofficially we do, because we also set up their LLC and got them their EIN #. But hopefully you get the point I am trying to get across.